On the accuracy of finite difference schemes for beam problems in the elastic range

Abstract

The finite difference method is applied to derive approximate solutions for the bending line of Euler-Bernoulli beam problems. The investigations are restricted to simple static configurations, i. e. straight beams with constant symmetrical cross-sections and constant elastic material properties. Only finite difference schemes of second-order accuracy are considered and special emphasis is given to the implementation of the boundary conditions. Based on comparisons with the exact solutions, clear recommendations can be given on the required number of nodes to obtain a certain accuracy in the numerical approach.